The Space and Rocket Center, of course
Drive up Monte Sano to the state park, and check out the zen garden and the view of downtown
I'd suggest the botanical garden, but the weather doesn't look like it'll be good for it.
Downtown is small, but pretty cool. The historic depot and art museum are on Church street.
Harrison Bros Hardware is on the south side of the courthouse.
If you have a chance, swing by
Bandito Burrito on Governor's Drive. I ate there religiously for nearly 8 years.
If you like German food, Huntsville has some of the best you'll eat anywhere (thanks to von Braun and his buddies settling in half a decade ago) -
Ol Heidelberg was the go-to when I lived there, but there are several other places.